نویسنده : امیر انصاری

1. $$
   x^2+10x+4=0
   $$
   
2. $$
   x^2-8x+13=0
   $$
   
3. $$
   3x^2+6x+1=0
   $$
   
4. $$
   -2x^2+4x+3=0
   $$
   
5. $$
   -0.1x^2 - 0.6x+0.4=0
   $$
   
6. $$
   0.5x^2-4x-6=0
   $$
   

پاسخ

1. $$
   x^2+10x+4=0\\
   x^2+10x=-4\\
   x^2+10x+25=-4+25\\
   (x+5)^2=21\\
   x+5=\pm \sqrt{21}\\
   x=-5 \pm \sqrt{21}
   $$
   
2. $$
   x^2-8x+13=0\\
   x^2-8x=-13\\
   x^2-8x+16=-13+16\\
   (x-4)^2=3\\
   x-4=\pm \sqrt{3}\\
   x = 4 \pm \sqrt{3}
   $$
   
3. $$
   3x^2+6x+1=0\\
   x^2+2x+\frac{1}{3}=0\\
   x^2+2x=-\frac{1}{3}\\
   x^2+2x+1=-\frac{1}{3}+1\\
   (x+1)^2=\frac{2}{3}\\
   x+1=\pm \sqrt{\frac{2}{3}}\\
   x=-1 \pm \frac{\sqrt{6}}{3}\\
   x = \frac{-3 \pm \sqrt{6}}{3}
   $$
   
4. $$
   -2x^2+4x+3=0\\
   x^2-2x-\frac{3}{2}=0\\
   x^2-2x=\frac{3}{2}\\
   x^2-2x+1=\frac{3}{2}+1\\
   (x-1)^2=\frac{5}{2}\\
   x-1 = \pm \sqrt{\frac{5}{2}}\\
   x=1 \pm \frac{\sqrt{10}}{2}\\
   x = \frac{2 \pm \sqrt{10}}{2}
   $$
   
5. $$
   -0.1x^2 - 0.6x+0.4=0\\
   x^2+6x-4=0\\
   x^2+6x=4\\
   x^2+6x+9=4+9\\
   (x+3)^2=13\\
   x+3=\pm \sqrt{13}\\
   x = -3 \pm \sqrt{13}
   $$
   
6. $$
   0.5x^2-4x-6=0\\
   x^2-8x-12=0\\
   x^2-8x=12\\
   x^2-8x+16=12+16\\
   (x-4)^2=28\\
   x-4=\pm \sqrt{28}\\
   x=4 \pm 2\sqrt{7}
   $$